Dynamic modeling and H ∞ independent modal space vibration control of laminate plates

Abstract

In this paper, combining the transfer matrix method and the finite element method, the modified finite element transfer matrix method is presented for high efficient dynamic modeling of laminated plates. Then, by constructing the modal filter and the disturbance force observer, and using the feedback and feedforward approaches, the H ∞ independent modal space control strategy is designed for active vibration control of laminate plates subjected to arbitrary, immeasurable disturbance forces. Compared with ordinary dynamic modeling and control methods of laminated plate structures, the proposed method has the low memory requirement, high computational efficiency and robust control performance. Formulations as well as some numerical examples are given to validate the method and the control performance. transfer matrix method, finite element, laminated plate, active vibration control, H ∞ control PACS: 46.70.De, 43.40.Dx, 43.40.VnIn recent years, the laminated plates have been widely used in various engineering applications, such as precision machinery, aircrafts, and vehicles and have attracted many researchers in fields of structural vibration analysis, damage detection, vibration control and noise control [1][2][3]. In terms of the dynamic performance and vibration control of laminated plates, the high-efficient dynamic modeling and appropriate control law design are the two key points. At present, the finite element method (FEM) has become the most powerful and most widely used tool for dynamic modeling of the laminated plate structures. Based on such a FEM model, many researchers studied many such vibration control design methods as the passive vibration control [4], velocity feedback control [5], linear quadratic regulator (LQR) approach [6], H 2 control [7], neural network control [8], fuzzy control [9], and intelligent algorithms [10].Generally speaking, when using the FEM model to study the dynamics and vibration control of the laminate plate structure, we often have to face the following problems.First of all, the FEM must use a large number of nodes, which results in the huge degrees of freedom (DOF) and the high orders of matrices in the global dynamic equations. Most modern control design methods, such as LQR, H 2 and H ∞ , tend to generate a controller of the order comparable to that of the global dynamic equations of controlled object. For a FEM model of the laminate plate, the large number of DOFs poses great difficulty for control system design. Even if one can get a controller from the full model, a very high order of the controller makes it infeasible for real-time implementation [1]. Secondly, the high matrix orders and large stiffness gradients of laminate plate would result in some numerical difficulties when the vibration characteristics are computed. The precise computation of vibration characteristics is the precondition for optimal design of a close-loop controlled system. Moreover, the robustness problem, which is caused by the discrepancy of modeling from the system identification error, d...

Solar Flare Prediction Model with Three Machine-learning Algorithms using Ultraviolet Brightening and Vector Magnetograms

“…To deal with the data, several machine-learning algorithms (see an introductory text to machine-learning, e.g., Hastie et al 2009) have been applied to the flare prediction problem: a neural network (Qahwaji & Colak 2007;Colak & Qahwaji 2009;Higgins et al 2011;Ahmed et al 2013), C4.5 decision trees (Yu et al 2009(Yu et al , 2010, learning vector quantization (Yu et al 2009;Rong et al 2011), a regression model (Lee et al 2007;Song et al 2009), k-nearest neighbor (Li et al 2008;Huang et al 2013;Winter et al 2015), a support vector machine (SVM) (Qahwaji & Colak 2007;Bobra & Couvidat 2015;Muranushi et al 2015), a relevant vector machine (AlGhraibah et al 2015), SVM regression , and an ensemble of four predictors (Guerra et al 2015). However, the best algorithm for flare prediction has not been discussed in previous works, and it cannot be found without directly comparing the performances of different algorithms.…”